Khan.scratchpad.disable(); To move up to the maestro level in his piano school, Michael needs to master at least $106$ songs. Michael has already mastered $15$ songs. If Michael can master $9$ songs per month, what is the minimum number of months it will take him to move to the maestro level?
To solve this, let's set up an expression to show how many songs Michael will have mastered after each month. Number of songs mastered $=$ $ $ Months at school $\times$ Songs mastered per month $+$ Songs already mastered Since Michael Needs to have at least $106$ songs mastered to move to maestro level, we can set up an inequality to find the number of months needed. Number of songs mastered $\geq 106$ Months at school $\times$ Songs mastered per month $ +$ Songs already mastered $\geq 106$ We are solving for the months spent at school, so let the number of months be represented by the variable $x$ We can now plug in: $x \cdot 9 + 15 \geq 106$ $ x \cdot 9 \geq 106 - 15 $ $ x \cdot 9 \geq 91 $ $x \geq \dfrac{91}{9} \approx 10.11$ Since we only care about whole months that Michael has spent working, we round $10.11$ up to $11$ Michael must work for at least 11 months.